Answer
$\dfrac{2}{2+\sin \theta}$; an ellipse
Work Step by Step
The polar equation of a conic with eccentricity $e$ and directrix $y=k$ is:
$r=\dfrac{ke}{1+e \sin \theta}$ ...(1)
We are given that the vertices are: $e=\dfrac{1}{2},k=2$
Then $y=2$
Thus, equation (1), becomes
$r=\dfrac{1}{1+(\dfrac{1}{2})\sin \theta}=\dfrac{2}{2+\sin \theta}$
